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Basic elements of arm postural controlanalyzed by unloading. Exp. Brain Res. 164:225-
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ARTICLE in EXPERIMENTAL BRAIN RESEARCH · AUGUST 2005
Impact Factor: 2.04 · DOI: 10.1007/s00221-005-2245-6 · Source: PubMed
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Mindy F Levin
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R E S E A R C H A R T I C L E
Philippe S. Archambault Æ Pavel MihaltchevMindy F. Levin Æ Anatol G. Feldman
Basic elements of arm postural control analyzed by unloading
Received: 15 September 2004 / Accepted: 23 November 2004 / Published online: 27 April 2005 Springer-Verlag 2005
Abstract To address the question of how arm posture iscontrolled, we analyzed shoulder–elbow unloading re-sponses in the horizontal plane for different directions of the initial load. The initial load, produced by a double-
joint manipulandum, was suddenly diminished to 1of 12randomly presented levels (60 to 10% of the initialload; in 6 out of 12 cases the final load direction variedby ±20). Subjects were instructed ‘‘not to intervene’’ inresponse to unloading. Neither the unloading onset northe final load level was predictable and we assumed thatthe responses to rapid unloading were involuntary.Unloading elicited a smooth hand movement charac-terized by a bell-shaped velocity profile. The changes inhand position, joint angles, and joint torques generallyincreased with greater amounts of unloading. For eachdirection of the initial load, tonic electromyographicactivity of the shoulder and elbow muscles also changed,
depending on the amount of unloading. The shoulderand elbow joint torques before and after unloading werea function of the difference between the actual configu-ration of the arm and its referent configuration (R)
described by the angles at which each joint torque waszero. The R configuration changed depending on thedirection of the initial load. Our electromyographic dataimply that these changes result from a central modifi-
cation of muscle activation thresholds. The nervoussystem may thus control the R configuration in a task-specific way by leaving it unchanged to generate invol-untary responses to unloading or modifying it toaccommodate a new load direction at the same initialposition. It is concluded that the R configuration is amajor variable in both intentional and involuntarycontrol of posture.
Keywords Unloading Æ Shoulder Æ Elbow Æ Posturalcontrol Æ Equilibrium-point hypothesis
Introduction
A basic objective of research in motor control is tounderstand how the nervous system, and the musculo-skeletal apparatus and afferent feedback, controls pos-ture in the presence of changing external forces. Posturalregulation includes adaptive reactions to sudden altera-tions in the load. In particular, in response to rapidunloading, the forearm moves to another position, withthe tonic electromyographic (EMG) activity of agonistmuscles decreasing and that of antagonists increasing sothat a lower net joint torque is generated to balance the
remaining load torque at the new position (Asatryanand Feldman 1965; Dufosse et al. 1985). Unloading re-sponses are generally considered to be postural reactionsmostly devoid of voluntary corrections, and thusresulting from the action of short- and long-latency re-flexes when constant values of reflex parameters (forexample thresholds and gains) are maintained by thecentral nervous system (Crago et al. 1976; Feldman andLevin 1995; Latash 1994).
In previous studies it has been shown that the changein elbow angle was augmented with increasing amounts
P. S. Archambault Æ A. G. FeldmanCentre de Recherche en Sciences Neurologiques,Universite ´ de Montre ´ al, Montreal,Quebec, H3S 2J4, Canada
P. Mihaltchev Æ M. F. LevinE ´ cole de Re ´ adaptation,Universite ´ de Montre ´ al,Montreal, Quebec,H3S 2J4, Canada
M. F. Levin Æ A. G. FeldmanCRIR, Institut de Re ´ adaptation de Montre ´ al,Universite ´ de Montre ´ al, Montreal,Quebec, H3S 2J4, Canada
P. S. Archambault (&)Dipartimento di Fisiologia Umana e Farmacologia,Universita ` di Roma ‘La Sapienza’,Piazzale Aldo Moro 5,00185 Rome, ItalyE-mail: [email protected].: +39-06-49910772Fax: +39-06-49910942
Exp Brain Res (2005) 164: 225–241DOI 10.1007/s00221-005-2245-6
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of unloading, thus producing a monotonic torque–anglecharacteristic (Asatryan and Feldman 1965; Levin andDimov 1997). For a given characteristic, tonic EMGsignals of agonists and antagonists disappeared or ap-peared, respectively, at specific elbow angles called theactivation threshold angles. Unloading from differentinitial elbow angles yielded similar characteristics butshifted along the angular axis so that the threshold an-gles were different for different characteristics (Asatryanand Feldman 1965; Levin and Dimov 1997; Fig. 1A).This implies that the voluntary movements necessary toreach the various initial positions before unloading wereassociated with a resetting of the muscle activationthresholds by neural control levels. In contrast, to pro-vide the involuntary EMG, force and kinematic re-sponses to unloading, control levels maintained
invariant values of muscle activation thresholds.Accordingly, the measured torque–angle relationshipswere called invariant characteristics (ICs) of the joint.Families of ICs have been recorded in humans for theelbow, knee, wrist, and jaw (Feldman 1966, 1979; Ostryet al. 1997). Similar families of characteristics, eachidentified by specific values of flexor and extensor acti-vation thresholds, have been recorded for differentmuscles in decerebrated cats (Feldman and Orlovsky1972; Matthews 1959).
These empirical findings underlie the k model formotor control, a version of the equilibrium-point (EP)hypothesis (Feldman and Levin 1995). According to thismodel, the nervous system would produce intentionalmovements by modifying muscle activation thresholds(k). Consistent with this hypothesis is the observationthat descending systems in the cat have the capacity toshift muscle activation thresholds (Feldman and Orlov-sky 1972; Nichols and Steeves 1986). With each resettingof the activation thresholds the system’s previous posi-tion appears as a deviation from the newly specifiedthreshold position. The same neuromuscular mecha-
nisms that produce EMG signals and forces in responseto deviations from the previous position will produceEMG signals and forces that oppose deviations from anewly specified position and thus will move the appro-priate body segments to it. In other words, by modifyingmuscle activation thresholds, control levels force theposture-stabilizing mechanisms to generate EMGactivity and muscle forces required for the transition to anew posture. In this sense, posture and movement stemfrom a single process.
To our knowledge, no attempt has been made tocharacterize unloading responses and record joint tor-que characteristics in a system with more than one de-
gree of freedom, although in modeling of double-jointarm movements the notion that the nervous system maycontrol posture and movement by changing muscleactivation thresholds, and thus shifting double-joint ICs,has been used (Flanagan et al. 1993; Gribble et al. 1998).Indirectly, the presence of ICs is supported by a study of the effects of perturbations of static arm postures(Shadmehr et al. 1993). It is necessary to directly verifywhether or not the results of the analysis of single-jointunloading movements can be extended to the double- joint system. To meet this objective, we used a double- joint manipulandum to specify and change an externalload and to determine, by the unloading method, ICs for
the shoulder–elbow system of the arm. In the single-jointcase, the relationship between joint torque and angle ismonotonic (Asatryan and Feldman 1965; St-Onge et al.1997). We expected that the same would be valid in thedouble-joint case. However, because of the presence of double-joint muscles and inter-muscular reflexes (Lac-quaniti and Soechting 1986; Nichols 1989), torque ateither the shoulder or the elbow would depend on both joint angles. Therefore, the IC of each joint shouldrepresent a surface relating torque to the two joint an-gles (Fig. 1B).
Fig. 1 Invariant torque–angle characteristics (ICs) for single-jointand two-joint systems (theoretical schemes). In (A), an IC (thicksolid curve) for a single joint is the sum of ICs (dotted curves) of twoopposing muscles groups, one of which starts generating activetorques at threshold angle k1and the other group at threshold anglek2. R represents the referent joint angle at which the net jointtorque is 0. The nervous system produces movement by shifting Rto R¢, thus setting another IC for that joint (thick dashed curve). In(B), two ICs (surfaces) of a two-joint system are shown. Each jointtorque is a function of both joint angles. The referent configurationof the arm (circle) is the combination of joint angles at which all joint torques are zero
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The k model provides a theoretical background fromwhich an additional prediction may be made. To balanceinitial loads acting in different directions but at the sameinitial arm position, the nervous system should specifydifferent double-joint ICs that should be separated fromeach other in angular coordinates and possibly differ interms of slopes. Therefore, by comparing different ICs,one can find parameters that remain invariant duringinvoluntary responses to unloading but are changed bydescending neural levels when subjects produce anintentional action to accommodate a new load directionat the initial position. Thus as in the case of single-jointexperiments (Asatryan and Feldman 1965), the presentanalysis in the double-joint arm may help to identifyintrinsic variables that are directly specified by the ner-vous system both in voluntary and involuntary controlof posture. Specifically, such a variable may represent areferent (R) configuration of the arm (Feldman andLevin 1995). In the absence of co-activation of opposingmuscle groups, it is the configuration at which all mus-cles of the arm reach their individual recruitmentthresholds (Feldman and Levin 1995). This configura-
tion is thus described by the set of threshold angles (onethreshold angle for each degree of freedom of the arm).Because of the threshold nature of the R configuration,the activity of each arm muscle will depend on thedeviation of the actual configuration of the arm from theR configuration. In other words, the difference betweenthese configurations is a global factor influencing all armmuscles, regardless of their biomechanical function. Inthe presence of muscle co-activation, the R configurationmay be operationally defined as the configuration atwhich arm muscles generate active forces that togetherproduce net zero torques. The R configuration is mod-ified by the nervous system to elicit movement or, if the
movement is mechanically prevented, to ensure isomet-ric torque generation.
Thus, the objectives of this study were:
– to characterize responses of the double-joint arm todifferent changes in the load; and
– to test the validity of the R concept by verifying that adifferent R configuration is specified when subjects arerequired to produce an intentional motor action—toaccommodate a change in the load condition at thesame initial position of the arm.
Methods
The procedure was approved by the local ethics com-mittee. Eleven right-handed subjects (7 men, 4 women;mean age±SD: 46±12 years) without any known neu-rological disorders participated in the experiment afterhaving provided their informed consent. Two of thesubjects had participated in earlier single-joint unloadingexperiments and were familiar with the objectives of thestudy. Their results did not differ from those in the othersubjects.
Experimental set-up
Subjects were seated in a high-backed chair and graspedthe handle of a custom built double-joint manipulan-dum. The height of the chair was adjusted so that themanipulandum’s handle was at the level of the shoulderand the subject’s arm moved in the horizontal plane.Subjects were strapped to the chair in order to limitmovement of the trunk. Their wrist and hand were sta-bilized using a wrist splint attached to the manipulan-dum’s handle. Arm movement was thus restrained toelbow and shoulder excursions in the horizontal plane.
Torque could be produced independently at each joint of the manipulandum through two torque motors(maximum torque 60 N m, or approximately 165 N atthe level of the manipulandum’s handle for the config-uration used in this experiment).
The manipulandum had a non-negligible mass that, if not compensated, could elicit a tendency of subjects tovoluntarily modify unloading responses. A softwareprocedure was developed to reduce the effect of rota-tional inertia on movement. Specifically, positive feed-
back was introduced in the torque output, based on theinstantaneous acceleration (recorded using accelerome-ters) and on the moment of inertia of each axis of themanipulandum. The feedback factor was selected, bytrial and error, to reduce inertia without introducingoscillations. The moment of inertia was measuredexperimentally for each segment of the manipulandumby applying a torque pulse of known value and mea-suring the angular velocity. This measurement was re-peated after the introduction of the inertia-correctingfeedback. The effective moment of inertia was reducedfrom 0.209 to 0.120 kg m2 (reduction of 62%) for theproximal limb of the manipulandum, and from 0.038 to
0.031 kg m2 (reduction of 18%) for the distal limb.Software for control of the experiment was developed
in Labview (version 5.1, National Instruments, Texas,USA).
Task
The general task was for subjects to bring and tomaintain the handle of the manipulandum at a specifiedinitial position while balancing an external load that wassubsequently reduced or removed. To achieve this,subjects viewed a cursor on a computer screen, corre-
sponding to the position of the handle in the horizontaltwo-dimensional workspace. They were instructed tobring the cursor to an initial target (0.5 cm red dot),which in external space corresponded to a point located30 cm in front of the sternum (mean initial elbow flexionangle: 101±7; shoulder flexion angle: 57±11). As thehand approached the target, an elastic load in one of fivedirections was generated by the torque motors. The loadresistance appeared at a distance of 10 cm from thetarget and attained its maximum value when the handreached the target. This combination of position and
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external load at the target constituted the initial condi-tion. After a random 2–4 s delay, the load was suddenlydiminished and the cursor on the screen disappeared.Subjects were instructed not to correct their armmovement when provoked by the change in load. Theythen had to hold the new arm position until the end of the trial (3 s). The paradigm involved unloading only,because sudden loading has been observed to causestretching of initially active muscles and the triggering of protective reactions such as co-activation of antagonistand antagonist muscles, possibly to prevent damage tocontractile fibers (Feldman 1979; Feldman and Levin1995; see also ‘‘Discussion’’ section).
To measure multiple torque–angle relationships, thedirection of the initial load was set so that subjects eitherhad to pull (0) or push (165) against it (Figs. 2A, B).We chose to use a load direction of 165 for pushing,because for 180 pilot studies had shown that someunloading conditions caused the subjects’ arm to hit thebody. Subjects performed all the unloading trials first forthe 0 load, then for the 165 load. The 0 load wassomewhat easier to handle and it was more convenient
for subjects to start the experiment with this load. Inaddition, 3 of the 11 subjects returned for a secondsession in which three different initial directions of forcewere used. These directions were selected so that theywere equally spaced between 0 and 165 (e.g., at 41,82.5 and 124). The magnitude of the load at the initialtarget corresponded to 30% of each subject’s maximumvoluntary force, measured before the experiment for thepushing and pulling directions. By specifying differentinitial load directions we implicitly induced subjects toproduce different intentional actions to bring the handto the same position before unloading while compen-sating for different loads. In terms of the k model, sub-
jects were forced to change parameters of their ICs toaccommodate the different initial conditions.
We used a large number of unloading conditions tobetter characterize the torque–angle surfaces resultingfrom unloading. For each of the initial loads there were12 unloading conditions. Six of these involved a changeof magnitude of the load while maintaining its initialdirection (unloading to 60, 40, 20, 10, 0, and 10% of the initial value). For the other six conditions, both themagnitude and direction of the load were changed inrandomly selected trials (unloading to 40, 20, and 10%of the initial value with a ±20 change in directionrelative to the direction of the initial load). Blocks of 12
trials were used in which each of the 12 final load con-ditions was presented once, in a random order to dis-courage anticipatory behavior of the subject. This wasrepeated six times, using a different ordering of theunloading conditions within each block (72 trials foreach initial load).
For two subjects, additional experimental conditionswere used. Unloading from the initial 0 or 165 loadswas produced with and without changes in the directionof the final load (unloading to 60, 40, 20, and 10%with a change in direction of either 0, ±20, or ±30
and to 10 and 0% with no change in the direction of theload), for a total of 22 conditions. Because the numberof trials was nearly doubled (132 trials for each initialload), the experiment for these two subjects was per-formed in two separate sessions, one for the 0 load andone for the 165 load.
Displacements provoked by sudden unloading areusually not corrected if the perturbation does not affectpostural stability, even if no specific instructions aregiven to the subject. The ‘‘unloading reflex’’ occursnaturally in naı ¨ve individuals and can be observed onthe first trial without any instructions (Crago et al.1976). It is on subsequent trials that they may attempt tointervene. To reinforce the natural behavior in repeatedtrials, subjects were requested ‘‘not to intervene’’ or ‘‘not
Fig. 2 Experimental procedures. In (A), the subject is maintainingthe initial load at the initial position, by producing a force (F), inone of five initial directions (0–165). After unloading, the subject’sarm moves to a new position (panel B displays an example for the0 load direction). In panel B, the convention used for measure-ment of shoulder and elbow flexion angle is shown (arrows). Inpanel C, a trial in which the subject voluntarily intervened is readilyidentified (thick line) by departure of the hand position–velocityprofile from a template (thin line; shaded area represents thestandard deviation) obtained from the average trajectory andvelocity from five other trials in the same experimental condition.The movements represent unloading to 20% of the initial load, inthe 165 direction
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to correct the effects of unloading’’. This meant lettingthe arm reach a final stable position and balance the newload without having to think about it. At first, the ten-dency to voluntarily react to unloading was generallystrong, and subjects typically needed 6–12 practice trialsto adapt to the task. Practice ended when subjects reli-ably produced movements containing a single peak inthe hand velocity profile for at least three consecutivetrials. Subjects practiced only a small subset of theunloading conditions. No training was necessary whenswitching the initial load direction.
Data recording
Kinematic data were sampled at 100 Hz using an Op-totrak system (model 3010, Northern Digital, Canada),with markers placed on the handle of the manipulandumand on bony landmarks of the right wrist (radial sty-loid), right elbow (lateral epicondyle of the humerus),and both shoulders (acromion) processes. Elbow flexionangle was calculated using the arccosine of the normal-
ized dot product of the vectors formed by the wrist andelbow markers, and the right shoulder and elbowmarkers, respectively. Shoulder horizontal flexion anglewas obtained likewise, using the horizontal componentsof the two vectors composed of the right shoulder andelbow markers, and by the left and right shouldermarkers, respectively. For the elbow, 0 corresponded tocomplete extension with values increasing with flexion.For the shoulder, 0 was defined as having the upperarm parallel with the vector formed by the two shouldermarkers, with positive values for rotations in the for-ward direction (Fig. 2B).
Torque applied to each of the manipulandum’s axes
was recorded with axial strain gauges. Using basicgeometry of the arm–manipulandum system, kinematicand kinetic data were used to calculate the force appliedat the level of the handle, and elbow and shoulder tor-ques. Because the joint torques were derived from thestrain-gauge data on the manipulandum’s axis, they arevalid in the static case only, i.e. before and after move-ment. Accurate estimation of joint torques duringmovement would have required taking into account thedynamics of the arm–manipulandum system (inertia,elasticity, viscosity), which was unnecessary, because wewere mostly interested in steady states of the arm beforeand after unloading.
Finally, we measured EMG activity using silver-pla-ted bipolar surface electrodes and Grass amplifiers forthe following muscles on the right side of the body:brachioradialis and anconeus (BR and AN, elbow flexorand extensor), pectoralis major and posterior deltoid(PM and DP, shoulder horizontal flexion and exten-sion), biceps and triceps brachii (BB and TB, double- joint flexor and extensor, respectively). The signals werefiltered at 5–500 Hz and sampled at 1,500 Hz. They werethen filtered offline using a 55–500 Hz third-order But-terworth filter to remove motion artifacts.
During offline analysis, trials in which the subjectsintroduced a voluntary correction were identified visu-ally from the presence of multiple peaks in the handphase diagram (position vs velocity plot) and were ex-cluded from further analysis (Fig. 2C). On average,11±5 of 144 trials (the number after ‘‘±’’ is standarddeviation, SD) were rejected for each subject (range: 3– 21 trials). There were no statistical differences betweenthe number of rejected trials in the five initial loadconditions.
Data analysis
Final endpoint positions obtained in the variousunloading conditions were compared using a modifiedKolmogorov–Smirnov test. This non-parametric proce-dure compares arbitrary two-dimensional distributionsby dividing the data into quadrants, then comparing theproportion of each distribution falling within eachquadrant (Peacock 1983; Fasano and Franceschini
1987).The relationship between joint torques and joint an-gles obtained during unloading from the same initialconditions was estimated using a planar fit:
T eT s
¼
Aee Aes
Ase Ass
Qe
Qs
C eC s
ð1Þ
where T e and T s represent elbow and shoulder torque,Qe and Qs are elbow and shoulder angles, respectively,and Aij and C i are coefficients. Data points were ob-tained by averaging the final joint torques and angles forall trials in each of the 12 unloading conditions. Anadditional point was obtained by averaging the initial
values of joint torques and angles for all 72 trials. Thus,13 points where available for each fit, except for the twosubjects who worked under additional unloading con-ditions, where the data were fitted using 23 experimentalpoints. It should be noted from Eq. 1 that two planeswere fitted, one for the elbow and one for the shoulder.Thus, each regression plane had three parameters andtherefore eight degrees of freedom (n31), or 18 de-grees of freedom for the subjects who performed addi-tional unloading conditions. To assess the quality of theregressions, 95% confidence intervals were calculatedfor the fitted planes.
Initial and final tonic EMG values (before and after
removal of the load) were assessed by computing theroot-mean-square average for two 100-ms windowscentered at 0.25 s before and 2 s after unloading. Toverify that voluntary corrections produced no systematiceffect in the remaining trials, an analysis was performedbased on the inter-trial variability of the tonic EMGdata. We assumed that, if subjects did not intervene, thechanges in tonic EMG activity would result from reflexreactions to unloading and, as a consequence, the inter-trial SD of the tonic EMG obtained after a particularunloading condition should be comparable with the
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inter-trial SD before the change in load. However, as formany biological signals, the SD of EMG data is notconstant but tends to vary linearly with magnitude.Thus, we opted to compare the coefficient of variability(CV; SD divided by the mean value) of the tonic EMGvalues.
Results
Hand kinematics
Sudden removal of the load induced a smooth transitionto a new hand position and configuration during a timethat was typically less than 1 s (Fig. 3). The hand movedin a direction opposite to that of the load (maximumpeak velocity of approx. 0.5 m s1 for unloading to10% of the initial load; Table 1). The horizontal dis-placement and peak velocity of the hand, and the totalmovement time, increased with the amount of unloadingfor each of the three directions of the final load (Fig-s. 3A–D). This was the case for all subjects and for all
five directions of the initial load.Joint angles and torques were likewise graded with
the amount of unloading for each of the five directionsof the initial load (Figs. 3G–L). The only exception fromthis rule was for the elbow angle and torque when the165 load was used with no change in the direction of residual loads. In these cases the amplitude of elbowmovements was small (subject mean±SD: 8±9), whichcan be explained by the low initial elbow torque (subjectmean±SD: 0.3±1.5 N m). However, when the direc-tion of the final load was changed by±20, substantialload-dependent changes in elbow angle and torque wereobserved (Figs. 3I, K and Table 1). The range of elbow
and shoulder motion was of the order of 10–20,depending on the direction of the initial load. Thedirection of changes in the joint angles varied with thedirection of the initial load (Table 1). For the 165 loaddirection elbow extension was observed in eight subjectsand flexion in three. Overall, the variety of both theinitial and final load conditions induced a broad rangeof changes in joint angles and torques.
Each transition to the final hand position was pro-duced by a single main movement, as can be seen by thepresence of a single large peak in the velocity profilesand of a single large loop in the phase (velocity vs po-sition) diagrams (Fig. 3C–F). The transition was char-
acterized by a bell-shaped velocity profile and wasusually followed by damped oscillations of the handaround the final position.
Although the unloading conditions were randomlypresented, hand trajectories were qualitatively similarfor the same change in load (Fig. 4A). The differentmovement data (movement time, peak velocity, distancetraveled, joint angles and joint torques) and EMGactivity were likewise qualitatively reproducible for thesame subject and unloading condition (see also the errorbars in Figs. 3, 6, 9 and 10). For all subjects the mean
inter-trial variability ranged from ±0.9 cm in the 60%unloading condition to ±2.6 cm in the 10% unloadingcondition for the x dimension (0). For the y dimension,the variability ranged from ±0.6 to ±1.2 cm (60 to10% unloading condition, respectively). These valueswere the same for all directions of the initial load.
Different levels of unloading without any change inload direction brought the hand to final points locatedon the same curve at distances gradually increasing withthe amount of unloading (circles in Fig. 4B). When thedirection of the residual load changed by ±20, thehand trajectory deviated from that obtained without achange in load direction. This effect was especially evi-dent for the 165 condition (Fig. 4B, left panel).
The distributions of final endpoint locations werecompared using the modified Kolmogorov–Smirnov testfor binary distributions (see ‘‘Methods’’ section). Toaccount for differences in the level of the initial loadbetween subjects, the position data were normalized tothe maximum excursion recorded for each subject. Wecompared the distributions of endpoint positions foradjacent levels of unloading for conditions in which all
subjects participated: separate tests were made for theinitial 0 and the 165 loads and for the three directionsof the final load. We then compared the distributions infinal hand position between the 60 and 40% unloadingconditions, the 40 and 20% conditions, etc. All com-parisons were significant at P<0.01 for the 165 initialload. For the 0 initial condition, endpoint distributionswere significantly different except between the 10 and0% final load conditions (P<0.2 in that case).
Invariant characteristics
To verify our main hypothesis that each joint torque is afunction of both joint angles, we used a planar fit for theelbow and shoulder torque data (Eq. 1). Examples of theplanar fits obtained for the elbow and shoulder torqueswith the 0 and 165 loads are shown in Fig. 5, for asubject with 22 unloading conditions. For all subjectsand initial directions of the load, the elbow and shoulderplanar fits had high R2 values (Table 2). The regressionswere significant in all but one case (<2% of all cases).Moreover, the coefficients of fit obtained for each sub- ject for the various directions of the initial load werealways different, both for the elbow and the shoulder.This confirmed our second hypothesis that ICs are
condition-dependent.To understand how the shoulder and elbow ICs are
combined to provide the appropriate force at the level of the hand, we considered the intersections of the twosurfaces in Figs. 5A and B (shoulder and elbow ICs)with the plane of zero torque. These intersections areshown by the two lines in elbow–shoulder co-ordinatesin Fig. 6A, (thick lines). These lines represent the com-binations of joint angles where torque at the elbow(thick solid line) or shoulder (thick dashed line) is zero.The two lines separate the angular space into four areas
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where shoulder and elbow torques are either positive ornegative. The long arrow indicates the direction of po-sitive shoulder and elbow torques. For example, at anyconfiguration of the arm represented by a point withinthe quadrant indicated by the arrow, the net joint torqueat the shoulder and elbow is positive and increases withthe distance between that point and the respective zero-torque line. The initial elbow angle for this subject isvery close to, and the initial shoulder angle is far from,
the zero torque elbow and shoulder lines (filled square inFig. 6A). This is consistent with the observation that, atthe initial arm configuration for this subject, near zeroelbow torque was combined with substantial positiveshoulder torque (Fig. 6A). For the 0 load direction, theinitial configuration was characterized by negative tor-que at the shoulder and elbow (Fig. 6D).
The intersection between the zero-torque lines (opencircles in Fig. 6) is of special interest. By definition, this
Fig. 3 Unloading produced asmooth transition of the armfrom the initial position to afinal position. Curves representthe mean of all six trials in eachexperimental condition for onesubject (thick curve is for thetrials in which the load wascompletely removed). Graphs inthe left column are unloadingresponses for the 165 initialload condition when thedirection of the final load
changed by +20 with respectto that of the initial load(unloading to 40, 20, 0 and10% of the initial load).Graphs on the right areresponses for the 0 initial loadcondition. No change in thedirection of the final load wasmade for any of unloading steps(unloading to 60, 40, 20, 10, 0and 10%). Error bars indicatethe inter-trial standarddeviation, for the condition inwhich it was the largest. Arrowson the right side of each graphindicate increasing amounts of
unloading. Bottom panels (K,L) show mean static jointtorques obtained beforemovement onset (I ) and afterthe transition of the arm to thefinal position for each amountof unloading (numbers from 60to 10, in %)
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is the point in angular space where both elbow andshoulder torques are null. It is also the configurationthat the arm reaches when the initial load is completely
removed (see Figs. 6b, d for the arm configuration inCartesian space). In terms of the EP hypothesis, this isthe point that describes the referent configuration of thearm (see ‘‘Introduction’’ section). The existence of unambiguous surfaces describing the relationships be-tween joint torques and joint angles (Fig. 5) shows thatthe net muscle torques can be expressed as a function of the difference between the referent configuration (R) andthe actual configuration of the shoulder–elbow system(Q):
T ¼ f ðQ RÞ
where
T ¼ T e
T s
ð2Þ
Specifically, for the linear approximation describedby Eq. 1 for muscle torques,
T eT s
¼
Aee Aes
Ase Ass
Qe
Qs
Re
Rs
ð3Þ
with Re
Rs
¼
AssC e AesC s AeeC s AseC e
Ase Aes Aee Assð Þ1 ð4Þ
The mean regression coefficients for all subjects areshown in Table 3, as expressed in the form of Eq. 3. Theerrors in Re and Rs were calculated using the 95%confidence intervals of the regression planes (Fig. 6a)and are reported in Table 3 (Erre, Errs). The regressioncoefficients were analyzed statistically between subjects,but only for the 0 and 165 conditions where thenumber of subjects was sufficiently high. The referentconfigurations (Re, Rs) constitute two-dimensional dis-
tributions that were significantly different from eachother according to the initial load condition (modifiedKolmogorov–Smirnov test; P<0.001). The comparisonof the slope coefficients yielded a significant differencefor Aee and Ase (paired t-tests; P<0.05). Thus dependingon the direction of the initial load, not only the referentconfiguration was modified but also the slope of theshoulder and elbow ICs. The R configurations of allsubjects for these two initial load conditions are alsoillustrated in Fig. 7.
To analyze the resultant force at the level of the handdue to the interaction of the elbow and shoulder ICs, wecomputed the forces at each point in space in a
25 cm·30 cm grid using a simple planar two-joint modelof the arm (Figs. 6C, F). We first calculated the elbowand shoulder angles required to position the hand ateach point within the grid. From these angles, we ob-tained the joint torques from the ICs using Eqs. 3 and 4.The magnitude and direction of the force at the level of the hand were then computed from the joint torques andangles. In Cartesian space, the planar ICs are equivalentto a force field that directs the hand towards the referentpoint, i.e., the arm to its referent configuration. Thecombination of different joint ICs for the 0 and 165
Table 1 Group means for arm-movement variables after unloading
Direction
Pull (0) 41 82.5 124 Push (165)
Initial load (N) 21.9 (7.9) 24.3 (5.9) 25.5 (5.7) 26.8 (5.5) 26.5 (9.5)Movement duration (s) 1.05 (0.16) 0.99 (0.13) 0.81 (0.03) 0.86 (0.03) 0.92 (0.16)Peak velocity (m s1) 0.49 (0.14) 0.69 (0.12) 0.78 (0.13) 0.57 (0.05) 0.50 (0.16)Displacement (m) 0.27 (0.12) 0.24 (0.06) 0.18 (0.05) 0.15 (0.04) 0.19 (0.06)Elbow movement Ext. Ext. Ext. Ext. Ext./flex.
Shoulder movement Abd. Abd. Add. Add. Add.D Elbow angle () 19.6 (15.0) 21.4 (6.9) 24.0 (7.5) 20.4 (7.2) 17.1 (12.8)D Shoulder angle () 17.7 (7.6) 8.8 (2.5) 7.5 (2.2) 10.5 (3.6) 20.1 (7.6)D Elbow torque (N m) 3.8 (1.3) 8.0 (2.1) 9.5 (2.3) 7.0 (1.5) 4.6 (3.4)D Shoulder torque (N m) 5.1(1.6) 3.9(1.2) 3.6(1.1) 7.4(1.8) 8.4 (3.6)
Numbers indicate inter-subject means (standard deviation). Formovement duration, peak velocity, and displacement, the maxi-mum values within all unloading conditions are reported. D:
maximum amplitude of change in joint torque or angle within allthe unloading conditions (maximumminimum). For 165 and 0,n=11 subjects; for the other directions n=3
Fig. 4 Hand trajectories for different unloading conditions. AIndividual traces for one subject (0 load condition) demonstratethat the hand followed a similar path when unloading was madewithout any change in the direction of the final load. B Whenunloading involved not only a change in the amount of the load butalso in the direction of its action, different hand paths and finalpositions (averaged) were observed
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load led to the formation of hand force fields with dif-ferent orientations and referent points (Figs. 6C, F).
Hand force fields and the referent configurations in
joint space are also shown for one of the three subjectswho performed unloading from five different orienta-tions of the initial load (Fig. 8). Results for the othertwo subjects were similar. Qualitatively for the subject inFig. 8, both the orientation of the ICs (the direction of anormal vector to the plane) and their intersection withthe zero-torque plane (the referent arm configuration),and the shape of their associated hand force fields,varied according to the initial direction of the load.
EMG activity
Activity of arm muscles was recorded in all subjects forthe 0 and 165 load directions. EMG activity of all
muscles was modified in response to unloading (Fig. 9).For the shoulder, some muscles could be readily classi-fied as agonists or antagonists according to the criterion
that they produce torques in the same direction (agon-ists), or in the opposite direction (antagonists) to that of the recorded joint torque. In the pectoralis major(shoulder agonist in the 165 load condition), unloadingcaused a sudden decrease in activity, with sometimes asubsequent short duration burst (Fig. 9A). At the end of movement, the tonic activity was decreased comparedwith its initial value. In the posterior deltoid (antagonistat the shoulder joint to the 165 load), rapid unloadingelicited a short term burst of activity. An increase in thefinal tonic activity was observed for the larger changes inload. These results were reversed for the 0 condition,where posterior deltoid acted as agonist and pectoralis
major as antagonist (Fig. 9B). For the other elbow andshoulder muscles, a general classification into agonists
Table 2 Results of planar fits (mean R2 values) for elbow and shoulder torques as a function of joint angles
Pull(0)
41 82.5 124 Push(165)
Elbow 0.89 (0.11) 0.89 (0.06) 0.84 (0.04) 0.85 (0.04) 0.87 (0.13)Shoulder 0.78 (0.11) 0.78 (0.14) 0.84 (0.10) 0.84 (0.11) 0.84 (0.14)
Numbers indicate inter-subject means (standard deviation). For 165 and 0, n=11 subjects; for the other directions, n=3
Fig. 5 Torque-angle surfaces(ICs) identified in unloadingexperiments. The mean initialand final shoulder torques werefit to a plane, in torque– shoulder–elbow angle space, fora subject who performed thetask in 22 unloading conditions.The fitted plane is a measuredIC for the shoulder joint. Thethick line represents the 0-
torque line, or the intersectionbetween the regression planeand the zero torque plane.Panels A , B are for the 165load and C, D for the 0 load.Diamonds indicate the initialcondition (torque and jointangles)
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or antagonists could not be made: although muscles of individual subjects behaved in a consistent manner,there were differences across subjects in individual motorpatterns. This probably resulted from muscle redun-
dancy or biomechanical variations.To verify that the tonic activity of muscles was
changed due to the unloading movement, we comparedacross subjects the level of EMG before and after thecomplete unloading condition (unloading to 0%), usingpaired t-tests. For the initial 0 load, there was a sig-nificant change in tonic EMG in the BR and in all threeextensors (AN, TB, and DB). For the initial 165 load,BP, PM, and DP displayed significant changes in tonicEMG.
Inter-trial variability of tonic EMG
Trials with an obvious sign of voluntary corrections (thepresence of multiple velocity peaks in the hand move-ment) were rejected (see ‘‘Methods’’ section). To furtherverify that voluntary corrections produced no systematiceffect in the remaining trials, an analysis was performedbased on the inter-trial variability of the tonic EMGdata. Because the timing and the extent of the pertur-bation was unpredictable, an increase of the variabilitywould point toward a voluntary correction. Tonic EMGvalues and inter-trial variability of a representative
Fig. 6 Referent configurations of the arm for unloading in the 165and 0 load conditions. On the left, zero-torque lines are shown forthe elbow (solid ) and shoulder joints (dashed ) obtained from thetorque planar regressions (Fig. 5) for one subject, in the 165 (A)and 0 (D) load conditions. Dashed lines represent the 95%confidence intervals of the torque regression, projected on the zero-torque plane. Long arrows show the direction of increasing torque.The empty circles represent the referent configuration, or thecombination of joint angles where both elbow and shoulder jointtorques are null. The filled squares show the initial arm configu-
ration, before unloading. The referent configurations of the arm ( B,E; solid lines) where different for the 165 and 0 conditions, for asimilar initial configuration (dashed lines). The hand force fields (C,F), computed based on the joint torque ICs (see ‘‘ Results’’ section)were also different for the two directions of the initial load. Errorbars represent, for the initial position, one standard deviation of theinitial joint configuration or hand position. For the referentconfiguration, the error bars in B and C are a transposition inCartesian space of the confidence intervals shown in A. When notshown, the error bars were smaller than the symbols
Fig. 7 Referent configurations in all subjects for the 165 ( filled squares) and 0 load conditions (empty circles). Shown are referentvalues of joint angles relative to the initial joint angles (0, 0) and the95% confidence ellipses of the distribution. For each data point,the respective zero-torque lines are shown for the elbow ( thick) andfor the shoulder (dotted ) joints; arrows show the direction of positive torque
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subject are shown in Figs. 10A, B. We first verified thatthe inter-trial coefficient of variability (CV) of the tonicEMG obtained after the 12 different changes in loadwere normally distributed using the Lilliefors test. Thisanalysis was performed for each subject, muscle, andinitial load direction and revealed that the final CVswere normally distributed for 124 out of 132 cases(94%). For the final CVs with a normal distribution, we
then checked that the initial inter-trial CV was within the95% confidence interval (Figs. 10C, D). This was truefor 120 out of 124 cases (97%). It can thus be said thatthe inter-trial CV of the tonic EMG remained constantbefore and after unloading. We therefore felt confidentthat subjects complied with the instruction to notintervene voluntarily following the change in load.
Threshold mechanisms of muscle activation and control
It has been suggested that a threshold mechanism of activation/deactivation of muscles is an essential deter-
minant of motor behavior and that central resetting of the arm position at which the muscle activation thresh-olds are reached underlies the changes in the referentconfiguration and voluntary motor actions (Feldmanand Levin 1995). That the threshold mechanism wasfunctional in the present experiments could be demon-strated in two ways. First, the EMG patterns observedin the present study suggest that the adjustment of the
motor performance to the new initial condition wasassociated with a change in the muscle activationthresholds. This follows from the finding that somemuscles become active while others became silent whenthe direction of the initial load changed (Figs. 9 and 10).In particular, between subjects, there was a significantchange in the initial tonic activity levels of all six re-corded muscles, when compared for the 0 and the 165load directions (paired t-tests, P<0.05). Because themuscle lengths were approximately the same in the twoconditions, the transition of the respective muscles to thesupra- threshold or sub-threshold state could beachieved by appropriate changes in the threshold muscle
Fig. 8 Hand force fields andreferent arm configurations forfive directions of the initialload, for one subject. The initialand the referent armconfigurations and respectivehand positions are shown,respectively, by squares andcircles in the hand (A – E) and joint (angular) workspaces (F).In (F), numbers indicate thedirection of the initial load; therespective zero-torque lines areshown for the elbow (thick) andfor the shoulder (dotted ) joints;arrows show the direction of positive torque. One can seethat the points representing thereferent configurations arelocated differently from thepoint (square) representing theinitial configuration of the arm
Table 3 Group means for stiffness-dimensional coefficients, referent joint angles and error on referent angles
Pull (0) 41 82.5 124 Push (165)
Aee 6.9 (5.4) 13.1 (1.5) 22.6 (5.1) 17.6 (6.7) 16.6 (6.0)*
Aes 6.3 (2.7) 14.0 (3.2) 13.0 (8.8) 1.5 (6.0) 3.8 (8.7)Ase 9.7 (10.8) 3.8 (2.0) 3.2 (1.6) 5.6 (2.5) 2.8 (7.3)*
Ass 16.5 (10.7) 25.3 (3.0) 20.3 (5.4) 24.4 (4.0) 19.7 (7.1)Re 86.1 (11.8) 92.8 (4.6) 94.3 (5.0) 98.3 (4.8) 87.9 (9.3)Rs 40.4 (12.0) 52.6 (4.0) 62.6 (9.0) 77.2 (8.8) 79.1 (13.2)E e 3.8 (3.3) 1.1 (0.3) 2.6 (2.3) 2.1 (1.4) 2.8 (1.3)E s 6.1 (5.8) 6.1 (2.4) 6.2 (0.8) 2.8 (2.5) 1.5 (1.1)
Numbers indicate mean (standard deviation). Values are in N m rad1 for Aii and in degrees () for R i and E i . * Significant difference
between the 0 and 165 directions (paired t-test, P<0.05). For 165 and 0, n=11 subjects; for the other directions, n=3.
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lengths. This shows that subjects did produce a task-dependent adjustment of muscle activation thresholds.
Second, after complete unloading the arm reached areferent configuration when muscles generated net zerotorques. These configurations were different dependingon the initial conditions (Fig. 8). The presence of co-
activation of muscles might cover-up a difference inmuscle activation thresholds at these configurations. Inthis situation, the difference in thresholds could bemanifested by shifts in the arm position at which aminimum in the EMG activity of each arm muscle isreached. Such shifts were regularly observed in thepresent study. It can be seen (Fig. 11) that the armconfigurations at which minimum EMG activity wasobserved for the two initial load directions (0 and 165)were clearly different for each of the six arm muscles.This further suggests that the activation thresholds forthe six muscles were related to the direction of the initialload (see ‘‘Discussion’’ section).
Discussion
Basic findings
When subjects were instructed not to intervene, suddenunloading of the shoulder–elbow system provoked anarm movement to a new steady state configuration. Thefinal configuration of the arm depended on the amountof unloading and on the direction of the load at the
initial position. For each of the five initial load direc-tions the net joint torque (T) was a function of the dif-ference between the actual (Q) and the referentconfiguration of the arm (R), the configuration at whichmuscles generate zero net torques. The R was constantfor the whole set of responses to unloading for the same
initial condition but different for different initial condi-tions.
By changing the initial load direction beforeunloading, we implicitly forced subjects to intentionallymodify their control variables to accommodate thesechanges. Our results showed that these actions wereassociated with a resetting of the muscle-activationthresholds, a change in the referent configuration of thearm, and, as a consequence, a repositioning of the elbowand shoulder ICs in joint space, usually accompanied bya change in the slopes of the surfaces representing theICs. These intentional actions were also associated withshifts in the arm positions at which minimum EMG
activity of muscles occurred.
‘‘Do not intervene’’ paradigm
In this study, subjects were instructed ‘‘to not intervenevoluntarily’’ in response to rapid removal of the load. Inother words, they were asked to preserve the behavior(changes in the arm position) that occurs naturally,without specific instructions, when the arm is subjectedto unloading for the first time. It is usually believed that
Fig. 9 EMG activity of allmuscles for one subject (A forthe 165 and B for the 0condition). The EMG signalswere filtered using RMSaveraging, then averaged overmultiple trials. Only threeunloading conditions aredisplayed for each muscle:unloading to 60, 20 and 0% (topto bottom). The time of
unloading is indicated by thevertical dashed lines at 0.5 s.The error bars indicate thestandard deviation (inter-trial)during the tonic phase beforeand after unloading. The samescaling was used for the 165and 0 load conditions. Forabbreviations see ‘‘Methods’’section
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with the instruction ‘‘do not intervene’’, subjects issue nochanges in their control variables (Cesari et al. 2001;Feldman 1966; Feldman and Levin 1995; Latash 1994;Mah 2001). Unlike EMG signals (usually called ‘‘motorcommands’’), control variables symbolize the influenceof neural descending systems on specific parameters suchas the thresholds and gains of proprioceptive reflexes.Thereby, even when central commands are constant,EMG signals could vary because of reflex influences.Therefore, the EMG signals and movements evoked byunloading are not considered to be caused by localspinal reflexes in the absence of central descendinginfluences. Rather, they result from an integrative action
of constant descending commands and proprioceptive,reflex reactions involving spinal and possibly supra-spinal (e.g., trans-cortical) pathways.
In theory, subjects had ample time to change theircontrol variables during the task. Intentional changes inmovement can be detected 250–300 ms after the onset of load perturbations in the hand kinematics (Adamovichet al. 2001; Popescu and Rymer 2000) and after 100– 150 ms in the EMG signals (Crago et al. 1976). Whenthe subject knows the direction of the perturbation inadvance, EMG changes occur even earlier (70 ms;
‘‘triggered reactions’’, Crago et al. 1976). It has beenshown that triggered reactions regularly occur in re-sponse to sudden loading of active muscles (Feldman1979). One possible cause of such reactions would be toprevent damage of sarcomeres following an abruptstretch of active muscles elicited by loading. Indeed,muscle injury and soreness occur after repeated eccentriccontraction (Lieber and Friden 1999).
To minimize the occurrence of triggered changes inthe control variables, loading was not used in the presentexperiments and, in addition, randomized trials wereused to discourage subjects from predicting the amountand timing of unloading. A small number of trials in
which subjects corrected responses to unloading wasidentified and excluded from the analysis.
An additional test that subjects did not producevoluntary or involuntary (triggered) corrections of re-sponses to unloading in the present study was based onthe known observation that such corrections cause alarge variability in the final position especially when theperturbation is unpredictable (Crago et al. 1976; Latash1994). Instead, for each unloading condition, weobserved consistent final hand positions, and joint tor-ques and EMG activity. In addition, an expected result
Fig. 10 Tonic EMG values and inter-trial variability of a singlesubject for the 165 (A, C) and for the 0 initial load (B, D). PanelsA and B illustrate the initial tonic EMG values (init) and the finalvalues for two muscles in each unloading condition. Numbers onthe x-axis indicate the percentage of the final load, and bars aregrouped according to each possible direction of the final load (0,+20 and 20, relative to the direction of the initial load). Errorbars indicate the inter-trial variability. The tonic EMG values werenormalized to the maximum observed value (initial or final). In C
and D, the distributions of the coefficients of variability ( CV ) intonic EMG are displayed for all muscles of the same subject shownabove. Each data point (·) indicates the inter-trial variability intonic EMG after one unloading condition. The mean of the finalCVs and the initial CV are also displayed. Error bars indicate the95% confidence interval of the mean final CV . An asterisk (*) afterthe muscle labels indicates a normal distribution of the final COVs(Lilliefors; P<0.05). For muscle abbreviations, see ‘‘Methods’’section
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of voluntary and involuntary (triggered) correctionswould have been the observation of substantial vari-ability in the EMG responses to changes in the load. Incontrast, we found that the coefficient of variation in thetonic EMG signals remained invariant regardless of theamount of unloading, for all muscles, and was indis-tinguishable from that of EMG signals before unload-ing. This result implies that, if present, corrections of responses were minor, and thus insignificantly influencedour results and conclusions. Thus several findings in thepresent study support the assumption that the subjectsfollowed the instruction to not intervene voluntarily inresponse to unloading. Finally, subjects only needed a
few practice trials to reliably accomplish the taskaccording to the instructions, also implying that littlelearning was involved and that voluntary correctionswere absent.
Role of muscle elasticity, proprioceptive reflexes,and descending control signals
Passive muscle forces produced in the absence of acti-vation could play an, albeit minor, role in our observedresponses to unloading. Passive elbow muscles producetorques that change approximately linearly in the range
between 20 and 130 of flexion, with zero net torquesoccurring in the middle of the whole biomechanicalrange of the elbow (Feldman 1979). The elasticity con-stant of passive elbow muscles is about 2.0 N m rad1,which is much less than that observed in our study. Thevalues characterizing passive resistance of shouldermuscles are not known, but one can expect they are of the same order of magnitude as for the elbow muscles.Thus, changes in active, rather than passive, joint tor-ques played a mayor role in the responses of the arm tounloading. This is corroborated by the observation that
unloading resulted in significant changes in the tonicEMG activity of most of the muscles studied. Thisobservation also rules out the possibility that the ner-vous system simply specified a constant level of muscleactivation and thus relied solely on the elasticity of ac-tive muscles in responses to changes in the load.
In general physiological terms, our basic results canbe explained in the following way. According to currentviews, proprioceptive reflexes are not fixed entitiescharacterized by unambiguous stimulus–response rela-tionships. Rather, they are comparatively complexstructures, the parameters of which are tuned by thecentral nervous system in a task-specific way (e.g., Houk
1976). All kinematic and EMG responses to unloadingfrom the same initial position and load direction prob-ably resulted from proprioceptive or, more generally,somato-sensory reflexes while their parameters specifiedby descending systems were kept constant (as implied bythe instruction to not intervene). To compensate for anew initial load acting in a different direction (e.g., 165)the threshold lengths at which muscle activation beginswere increased for those muscles that counteracted theprevious load. The actual lengths of these muscles nowappeared to be below thresholds and muscles becamesilent (e.g., posterior deltoid in Fig. 9). At the same time,the threshold lengths were decreased for muscles coun-
teracting the new load. The actual length of these mus-cles now appeared to be above thresholds and the musclebecame active (e.g., PM in Fig. 9).
We can assume that the nervous system, by specifyingappropriate muscle thresholds, selected a set of coordi-nated proprioceptive reflexes in order to oppose theinitial load and achieve the responses observed in thisstudy. However, because of the redundant number of muscles, the nervous system could have selected manydifferent combinations of threshold lengths to producethe same initial force and oppose the initial load. Only a
Fig. 11 Joint configurations of all subjects where the minimumtonic EMG was observed forthe 165 ( filled squares) and 0load conditions (empty circles).Values are relative to the initial joint configuration (0, 0). The95% confidence ellipses of thedistribution are also shown andindicate that the jointconfigurations at which
minimum tonic EMG occurredchanged with different initialload conditions
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subset of those combinations leads to a stable solution,exemplified by the converging force fields in Figs. 6 and8. Producing single, smooth movements after load per-turbations may be desirable, for example, by allowingone to quickly recover. The idea that the nervous systemmakes uses of redundancy to select specific coordinationpatterns is also present in the ‘‘complex manifold’’hypothesis (Scholz and Schoner 1999; Scholz et al.2000).
Explanations in terms of the k model
In this study, we measured static angles and torques atthe level of the elbow and shoulder, both before andafter rapid removal of the load from an initial stable armposture. Our results are consistent with the concept of the referent arm configuration, associated with the no-tion that a deviation from the referent configurationevokes non-zero net torques increasing as a function of the difference between the actual and the referent con-figurations (Feldman and Levin 1995). For each initial
condition, this function describes transitions betweendifferent steady states resulting from unloading while thereferent configuration remains unchanged. In the k
model, the referent configuration is a major controlvariable underlying intentional movements. The invari-ance of this control variable for each of the torque–anglefunctions obtained by unloading justifies our referenceto them as to ICs.
Our main hypothesis that intentional actions areassociated with resetting the referent arm configurationwas also confirmed in the present study. This conclusionfollows from the finding that the torque–angle surfacesor ICs describing responses to unloading were shifted in
spatial coordinates when the direction of the initial loadwas modified, suggesting that to accommodate thesechanges in the motor task, control levels reset the ref-erent arm configuration. Likewise, the orientation of thehand force fields computed from the joint ICs differed,depending on the direction of the initial load. Similarforce fields were reported from the measurement of therestoring force after small passive displacements of thestable arm in the horizontal plane (Shadmehr et al.1993). These force fields were not the same for differentinitial arm positions, which implies, as have previousstudies of single-joint tasks (Asatryan and Feldman1965; Levin and Dimov 1997; Ostry et al. 1997), that
moving from one posture to another requires a spatialshift of the joint ICs. These results, together with thepresent data, imply that resetting of the referent armconfiguration is not only necessary to preserve the samehand position when the load direction changes but alsoto move the hand position to a new position. In otherwords, the present analysis addresses not only thequestion of which parameters remain invariant in re-sponse to unloading but also the question of whichparameters are controlled by the nervous system toproduce intentional movements or isometric torques.
The reason a linear fit was used to compute the jointICs is that a plane is the simplest three-dimensionalsurface, allowing for a small number of parameters.However, we do not mean to imply that ICs are gener-ally linear. Indeed, both active and passive musclecharacteristics are non-linear, so it is expected that ICsshould include non-linear terms also. For single jointmovements of the elbow and jaw, non-linear ICs havebeen reported (Asatryan and Feldman 1965; Ostry et al.1997).
Linear stiffness values, as measured by the fit coeffi-cients of the ICs, were of the same order as has beenpreviously reported when measuring the restoring forcesafter a small displacement of the static two-joint arm(Flash and Mussa-Ivaldi 1990; Gomi and Kawato 1997;Mussa-Ivaldi et al. 1985; Tsuji et al. 1995). However inthose studies, the cross terms Ase and Aes (the relation-ship between rotation at one joint with torque at theother joint) were found to be small when compared tothe symmetric terms Ass and Aee. This was confirmed inthis experiment for the 165 and the 124 conditions, butnot for the other three directions of the initial load,
where Aee, Ase and Aes had similar magnitude (Table 3).It may be indicative of greater involvement of double- joint muscles in movements generally directed towards0, compared with 165 or for the maintenance of astatic posture in the absence of an external force. Indeed,TB (a double-joint extensor) is at an advantage againstthe 0 load, because in this condition subjects generallyproduced extension torque at the shoulder and elbow. Inthe other conditions, subjects generally produced tor-ques of opposite directions at the elbow and shoulder, sothat neither the BB nor the TB could be at an advantage.
Taken together, our results are consistent with thefollowing explanations. To move the arm to the initial
position while balancing the initial load, the nervoussystem shifted muscle activation thresholds to theirvalues determined previously during the short-termpractice session of reaching the target in the presence of the same load. This control process set a referent armconfiguration, R, at which the system could generatezero joint torques. Because of the difference between theactual and the referent configurations, muscle activationand torques emerged tending to change the actual con-figuration, Q, in the direction minimizing the difference.The process was accomplished when the difference, QR, was reduced to a value that was just sufficient toprovide muscle forces required to balance the initial load
force when the hand reached the initial target. In re-sponse to unloading, the system maintained the same Rconfiguration thus relying on the ability of muscles’autogenic and heterogenic proprioceptive reflexes tobring the arm to an equilibrium position depending onthe residual load. To accommodate a change in theinitial load condition, the system specified a different Rconfiguration. This process could be combined with achange in the degree of co-activation of opposing musclegroups determined by the differences between theiractivation thresholds (k1 and k2 in Fig. 1a), which is
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consistent with the observation that the slopes of ICswere usually different for different initial conditions.
Alternative explanations
Experiments on adaptation to variable force fields haveled to the idea that the nervous system makes use of inverse dynamics models to explicitly calculate the jointtorques needed to produce movements along a desiredtrajectory while compensating for external forces (Bhu-shan and Shadmehr 1999; Kawato 1999; Wolpert et al.1998). It is also assumed that reflex and sensory sub-systems stabilize the on-going movement by providingfeedback with respect to the desired trajectory (Shad-mehr and Mussa-Ivaldi 1994; Wolpert et al. 1998). Thesemodels have primarily been designed to provide a de-sired trajectory for pointing, but not to specifically ex-plain the responses in a postural task, such as unloadingwith the instruction ‘‘do not intervene’’. Many authorsindeed consider that posture and movement, althoughlinked, are controlled separately by the nervous system
(e.g., Massion 1992). An alternative opinion is thatposture and movement would stem from the same neuralprocesses (Feldman and Levin 1995; Von Holst 1950).
In the context of our results, it is important to knowwhether or not the explanations of pointing movementsin the framework of internal models and inversedynamics force computations can be extended to includeunloading responses. In this framework, one can assumethat control levels first compute and then specify aconstant level of muscle activation and thus rely on theelasticity of active muscles to respond to changes in theload. This assumption conflicts with the observation thatthe EMG activity was load- and position-dependent in
the present experiments.Alternatively, one could accept the idea that posture
and movement are controlled separately. Thus, once theposition before unloading has been reached, the move-ment controller could abandon its inverse and forwardcomputations of muscle activation and torques andhand over control to the postural system. Thus, controllevels would let the muscle-reflex system manifest itsnatural, direct dynamical properties to provide the sys-tematic EMG, force and kinematic responses tounloading. This mixed strategy has recently been pro-posed to explain the decrease in muscle co-contractionfollowing learning of a novel motor task (Osu et al.
2002). A potential problem with this explanation is thatin our experiments, the final EP for reaching movementto match the initial load was at the same time a depar-ture point for unloading and thus belonged to the set of points comprising the joint ICs. Therefore, the tonicEMG level at the departure point of unloading had thesame dynamical, non-computational nature as at anyother point of the IC.
We would like to emphasize that we are not ques-tioning the ability of the neuromuscular system to dealwith external loads and adapt to new conditions based
on some predictive mechanisms or expected events in theenvironment. What is doubtful in the light of the presentresults and those from other studies based on unloadingexperiments (Asatryan and Feldman 1965; Biryukovaet al. 1999; Levin and Dimov 1997; Ostry et al. 1997) isthat the central nervous system uses internal modelsprincipally based on inverse dynamics computations, forthe control of both posture and movement. In contrast,the k model is able to explain unloading movements andalso applies to voluntary movement (see ‘‘Introduction’’section). A successful two degrees of freedom model of the arm was developed using the k model that correctlydescribes the kinematics and dynamics of point-to-pointmovement (Flanagan et al. 1993). Recently, this modelwas used to show how the nervous system could adapt tovelocity-dependent force-fields without needing toexplicitly compute the forces acting on the hand (Grib-ble and Ostry 2000). EP theory was also successfullyapplied to the study of multi-joint arm movement (Ce-sari et al. 2001; Latash et al. 1999), and whole-bodymovements (Domen et al. 1999; Feldman et al. 1998;Gunther and Ruder 2003; Lestienne et al. 2000).
Acknowledgements This work was supported by FRSQ (Fonds deRecherche en Sante ´ du Que ´ bec, Canada), CIHR (Canadian Insti-tutes of Health Research, Canada) and NSERC (Natural Scienceand Engineering Council, Canada). We would like to thank DrDavid Ostry for his helpful comments on the paper.
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